Here's how the Longman dictionary distinguishes the two senses of the noun 'conference'.
1 a large formal meeting where a lot of people discuss important matters such as business, politics, or science, especially for several days [for this sense, I assume, it's 'at a conference']
2 a private meeting for a few people to have formal discussions
Mr Dickson is in conference.
I find this distinction quite subtle and hardly significant at all. Please explain the difference in usage. In addition, I have no idea why there's no article in the second example given the fact that it's a countable noun. Even my spellchecker Grammarly objects.